Odor was hurt Tuesday night when his knee slammed into Houston catcher Martín Maldonado's head as he reached the plate and scored in the sixth inning of New York's 7-3 win.
Yankees manager Aaron Boone said Odor will be examined later Wednesday by head team physician Dr. Christopher Ahmad.
"I think all things considered, we kind of lucked out,'' Boone said. "It looked ugly to me right away, and I was pretty concerned. So I think it's going to be on the shorter side. I don't want to speculate until Dr. Ahmad kind of gives that prognosis, but I don't think it's going to be too long.''
Odor appeared to be trying to avoid DJ LeMahieu's bat, which was lying in the right-handed batter's box after he hit a soft grounder to third for an infield single. Odor came around when third baseman Alex Bregman overthrew first for an error.
Odor was acquired by the Yankees from Texas on April 6 and became a regular in the New York lineup with a coveted left-handed bat. The 27-year-old is hitting .164 with four homers and 11 RBIs.
The Yankees recalled right-hander Albert Abreu from Triple-A Scranton/Wilkes-Barre.